We have defined $$ \Delta E = \frac{1}{2} \langle \chi | \hat{M}| \chi \rangle $$ with the vectors $$ \chi = \left[ \delta C\hspace{0.2cm} \delta C^*\right]^T $$ and the matrix $$ \hat{M}=\left(\begin{array}{cc} \Delta + A & B \\ B^* & \Delta + A^*\end{array}\right), $$ with \( \Delta_{ai,bj} = (\varepsilon_a-\varepsilon_i)\delta_{ab}\delta_{ij} \).